derivative of (sin(x+cos(x))sec(x)dx)

Lösung

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

d ((cos (x) - sin (x)) sec (x) x + (x sec (x) tan (x) + sec (x)) (sin (x) + cos (x)))

Schritte zur Lösung

\frac{d}{d x} ((sin (x) + cos (x)) sec (x) d x)

Behandle

d

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= d \frac{d}{d x} ((sin (x) + cos (x)) sec (x) x)

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x) + cos (x), g = sec (x) x

= d (\frac{d}{d x} (sin (x) + cos (x)) sec (x) x + \frac{d}{d x} (sec (x) x) (sin (x) + cos (x)))

\frac{d}{d x} (sin (x) + cos (x)) = cos (x) - sin (x)

\frac{d}{d x} (sec (x) x) = x sec (x) tan (x) + sec (x)

= d ((cos (x) - sin (x)) sec (x) x + (x sec (x) tan (x) + sec (x)) (sin (x) + cos (x)))

\frac{d}{d x} (\frac{6 x}{x ^{2} + 2})

\int t^{2} - cos (2 π) t d t

\int sin^{2} (d) t

\frac{d}{d x} ((16 x)^{3})

d er i v a t i v e f (x) = - 2 sin (2 x)